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The variance of the average depth of a pure birth process converges to 7
- Publication Year :
- 2018
- Publisher :
- arXiv, 2018.
-
Abstract
- If trees are constructed from a pure birth process and one defines the depth of a leaf to be the number of edges to its root, it is known that the variance in the depth of a randomly selected leaf of a randomly selected tree grows linearly in time. In this letter, we instead consider the variance of the average depth of leaves within each individual tree, establishing that, in contrast, it converges to a constant, 7. This result indicates that while the variance in leaf depths amongst the ensemble of pure birth processes undergoes large fluctuations, the average depth across individual trees is much more consistent.
- Subjects :
- Statistics and Probability
60J80
010102 general mathematics
Probability (math.PR)
Process (computing)
Contrast (statistics)
Variance (accounting)
01 natural sciences
010104 statistics & probability
Statistics
FOS: Mathematics
Tree (set theory)
0101 mathematics
Statistics, Probability and Uncertainty
Constant (mathematics)
Mathematics - Probability
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....ea2c535e42c8f38a5093ae7e1c369484
- Full Text :
- https://doi.org/10.48550/arxiv.1812.05966